Stair Calculator — risers, run, and stringer

How it works

A stair converts a vertical rise into a comfortable walk, and every dimension follows from two choices: the total rise (the finished floor-to-floor height) and how deep each tread is.

Start with the risers. A comfortable step is about 7 in tall, so the number of risers is the rise divided by that target, rounded to a whole number:

steps = round(rise ÷ target riser)

The actual riser height is then the rise shared evenly over those steps — riser = rise ÷ steps — which is why it lands near, but rarely exactly on, the 7 in target. A flight always has one fewer tread than risers (the top riser lands you on the floor, not on a tread), so the total run is:

run = (steps − 1) × tread depth

The stringer is the sloped board the treads and risers are cut into. Because the rise and run form a right triangle, the stringer is the hypotenuse:

stringer = √(rise² + run²)

and the stair angle is arctan(rise ÷ run).

Comfort and safety are governed by building code. Under the 2021 IRC (R311.7.5), a residential riser may be no more than 7¾ in and a tread no less than 10 in; the 2024 IRC relaxed these to 8¼ in and 9 in. A long-standing rule of thumb for a comfortable stair is 2 × riser + tread ≈ 24–25 in. Always confirm the figures against the code your local jurisdiction has adopted.

Worked example

Take a 108 in floor-to-floor rise (a 9 ft floor height) with 10 in treads and a 7 in target riser. The rise needs round(108 ÷ 7) = 15 risers, each 108 ÷ 15 = 7.2 in tall — within the 7¾ in IRC limit. Fifteen risers means 14 treads, so the total run is 14 × 10 = 140 in. The stringer is √(108² + 140²) = √31,264 = 176.8 in, and the stair climbs at arctan(108 ÷ 140) = 37.6°.

Frequently asked questions

How many steps do I need for a given rise?

Divide the total rise by a comfortable riser height — about 7 in — and round to the nearest whole number: steps = round(rise ÷ 7). A 108 in rise gives 15 risers; a 96 in rise gives 14. Then the exact riser height is the rise divided by that number of steps.

What is a comfortable riser height?

Around 7 in is the sweet spot for most people. The 2021 IRC caps a residential riser at 7¾ in and requires the risers in a flight to be within 3⁄8 in of each other, so the calculator spreads the rise evenly rather than leaving an odd last step.

Is my staircase up to code?

Under the 2021 IRC (R311.7.5), each riser must be 7¾ in or less and each tread 10 in or more; the 2024 IRC uses 8¼ in and 9 in. This calculator reports the geometry — check the riser height and tread depth it gives against the code edition your jurisdiction has adopted, and confirm headroom, width and handrail requirements separately.

How long a board do I need for the stringer?

The stringer is the diagonal of the rise and run, so its length is √(rise² + run²). For a 108 in rise over a 140 in run that is √(108² + 140²) = 176.8 in, so a 16 ft board covers it with room to notch the treads. Order a little extra for the cuts.

What angle should a staircase be?

A typical interior stair sits around **30–38°** — the arctangent of the rise over the run. The example above climbs at 37.6°, near the steep end; deeper treads or a taller target riser lower the angle, while a tighter run raises it.

Why is there one fewer tread than risers?

The final riser lifts you onto the upper floor, which acts as the last "tread," so a flight with 15 risers has only 14 walking surfaces below it. Missing this off-by-one is the most common stair-layout error.